How to teach percentages using Proportions

Math For Life SituationsVicki Angel

Manuel A. Navarro

1. Understand Ratios2. Offer instructors an

effective, easy, relevant way to teach percents using the proportion method

Objectives:

WHAT IS A RATIO?

COMPARISON BETWEEN TWO QUANTITIES OR NUMBERS.

4 puzzle parts to 3 gears

WHAT IS THE RELATIONSHIP BETWEEN THEM?

For every 4 puzzle parts, there are 3 gears.

RATIOS CAN BE WRITTEN IN 3 DIFFERENT WAYS:

· 4 to 3

· 4 : 3

· 4 / 3

More about ratios

• Ratios can be reduced by division. Example: 6 / 4 = 3 / 2 when divided by 2 / 2

• Ratios can be increased by multiplication. Example: 6 / 4 = 18 / 12 when multiplied by 3 / 3

• Order is important. Example:

4 full time to 5 part time workers it is not the same as 5 part time to 4 full time workers

What is a proportion?

In a proportion there are 2 ratios combined by the equal sign ( = ).

This makes both ratios equivalent

For example:30 to 6 = 5 to 1How do we know?By cross multiplication30 X 1 = 6 X 5 30 = 30

How do you introduce Percents?

1. What is 20% of 40?2. 45 is 45% of what number?3. 35 is what percent of 70?4. Students get confused on

how to solve these problems!

1. When do I multiply?2. When do I divide?3. How do you multiply or

divide with percents?4. Please, give me an easy way

to do it!5. The answer is a

PROPORTION!

All percent problems are composed of three parts◦Percent◦Part◦Whole

The answer lies in identifying which one is missing.

Basics of Percents

Basic Proportion setup

isof

%100

Start with teaching students how to identify the three components using CLUE WORDS

◦Is – defines the part, or portion

◦Of – defines the whole or original amount

◦% symbol – defines percent

Basics of Percents

Identifying Components

8 is 20% of 40

PART

PER

CEN

T

WH

OLE

Clue Words◦ IS = Part, portion.◦ % = Percent Symbol◦ OF = Whole, original.

Identifying Components

8

is

of

%

100

is 20%

of 40

100IS

OF

%

2 & 3

Pages

DoLet’s try an exercise.

What is 20% of 40?

40

Using Proportion to find answers

?40

20%100Cross

Multiply

100

8

20

X = 800

Divide by the other number

= 8800÷

8

8 is 20% of what number?

Using Proportion to find answers

?20%100

Cross Multiply

40X = 800÷ =

8100

Divide by 3rd. Number

20

40

8

8 is what % of 40?

Using Proportion to find answers

40? %

100Cross Multiply

20X =800÷ =

8100

40

Divide by 3rd. Number

20

%

4 - 6

Pages

Do

Let’s continue our exercise.

1. Multiplication? Division?2. Eliminates the need to

convert percent into decimals.3. Introduces students to

variables.4. Fractions, Unit conversions

and Geometry applications.

Advantages:

1. Q & A. Are there any questions?

2. Do you have any suggestions?

3. Do you think this is something you can use?

THANK YOU!